Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 69584, 13 pages
doi:10.1155/JAMSA/2006/69584

On nondensely defined semilinear stochastic functional differential equations with nonlocal conditions

M. Benchohra,1 S. K. Ntouyas,2 and A. Ouahab1

 1Laboratoire de Mathématiques, Université Djillali Liabès – Sidi Bel Abbes, BP 89, Bel Abbes 22000, Algeria
2Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
Received 9 October 2004; Revised 5 March 2005; Accepted 7 March 2005

Abstract

The nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first-order semilinear stochastic functional differential equations in Hilbert spaces.